MAX15021
Dual, 4A/2A, 4MHz, Step-Down
DC-DC Regulator withTracking/
Sequencing Capability
Maxim Integrated | 16www.maximintegrated.com
As seen in Figure 4b, a Type II compensator provides for
stable closed-loop operation, leveraging the +20dB/
decade slope of the capacitor’s ESR zero, while extend-
ing the closed-loop gain-bandwidth of the regulator. The
zero crossover now occurs at approximately three times
the uncompensated crossover frequency, f
CO
.
The Type II compensator’s midfrequency gain (approxi-
mately 12dB shown here) is designed to compensate
for the power modulator’s attenuation at the desired
crossover frequency, f
CO
(Gain
E/A
+ Gain
MOD
= 0dB at
f
CO
). In this example, the power modulator’s inherent
-20dB/decade rolloff above the ESR zero (f
ZERO,ESR
) is
leveraged to extend the active regulation gain-band-
width of the voltage regulator. As shown in Figure 4b,
the net result is a three times increase in the regulator’s
gain bandwidth while providing greater than 75° of
phase margin (the difference between Gain
E/A
and
Gain
MOD
respective phases at crossover, f
CO
).
Other filter schemes pose their own problems. For
instance, when choosing high-quality filter capacitor(s),
e.g. MLCCs, the inherent ESR zero may occur at a
much higher frequency, as shown in Figure 4c.
As with the previous example, the actual gain and
phase response is overlaid on the power modulator’s
asymptotic gain response. One readily observes the
more dramatic gain and phase transition at or near the
power modulator’s resonant frequency, f
LC
, versus the
gentler response of the previous example. This is due
to the filter components’ lower parasitic (DCR and ESR)
and corresponding higher frequency of the inherent
ESR zero. In this example, the desired crossover fre-
quency occurs below the ESR zero frequency.
In this example, a compensator with an inherent midfre-
quency double-zero response is required to mitigate
the effects of the filter’s double-pole phase lag. This is
available with the Type III topology.
As demonstrated in Figure 4d, the Type III’s midfre-
quency double-zero gain (exhibiting a +20dB/dec
slope, noting the compensator’s pole at the origin) is
designed to compensate for the power modulator’s
double-pole -40dB/decade attenuation at the desired
crossover frequency, f
CO
(again, Gain
E/A
+ Gain
MOD
=
0dB at f
CO
) (see Figure 4d).
In the above example the power modulator’s inherent
(midfrequency) -40dB/decade rolloff is mitigated by the
midfrequency double zero’s +20dB/decade gain to
extend the active regulation gain-bandwidth of the volt-
age regulator. As shown in Figure 4d, the net result is
an approximate doubling in the controller’s gain band-
width while providing greater than 55 degrees of phase
margin (the difference between Gain
E/A
and Gain
MOD
respective phases at crossover, f
CO
).
Design procedures for both Type II and Type III com-
pensators are shown below.
MAGNITUDE (dB)
PHASE (DEGREES)
FREQUENCY (Hz)
-60
-40
-20
0
20
40
-80
-135
-90
-45
0
45
90
-180
MAX15021 fig04c
100 1k 10k 100k
1M 10M
10
|G
MOD
|
|G
MOD
|
ASYMPTOTE
f
LC
f
ESR
< G
MOD
Figure 4c. Power Modulator Gain and Phase Response with
Low-Parasitic Capacitor(s) (MLCCs)
MAX15021 fig04d
MAGNITUDE (dB)
PHASE (DEGREES)
FREQUENCY (Hz)
-60
-40
-20
0
20
40
60
80
-80
-203
-135
-68
0
68
135
203
270
-270
100 1k 10k 100k
1M 10M
10
< G
EA
|G
EA
|
|G
MOD
|
f
LC
f
ESR
f
CO
< G
MOD
Figure 4d. Power Modulator and Type III Compensator Gain
and Phase Response with Low Parasitic Capacitors (MLCCs)
MAX15021
Dual, 4A/2A, 4MHz, Step-Down
DC-DC Regulator withTracking/
Sequencing Capability
Maxim Integrated | 17www.maximintegrated.com
Type II: Compensation when fCO > fZERO,ESR
When the f
CO
is greater than f
ESR
, a Type II compensa-
tion network provides the necessary closed-loop com-
pensated response. The Type II compensation network
provides a midband compensating zero and a high-fre-
quency pole (see Figures 5a and 5b).
R
F
C
F
provides the midband zero f
MID,ZERO
, and
R
F
C
CF
provides the high-frequency pole, f
HIGH,POLE
.
Use the following procedure to calculate the compen-
sation network components.
Calculate the f
ESR
and LC double pole, f
LC
:
where C
OUT
is the regulator output capacitor and ESR
is the series resistance of C
OUT
. See the
Output-
Capacitor Selection
section for more information on cal-
culating C
OUT
and ESR.
Set the compensator’s leading zero, f
Z1
, at or below the
filter’s resonant double-pole frequency from:
Set the compensator’s high-frequency pole, f
P1
, at or
below one-half the switching frequency, f
SW
:
To maximize the compensator’s phase lead, set the
desired crossover frequency, f
CO
, equal to the geomet-
ric mean of the compensator’s leading zero, f
Z1
, and
high-frequency pole, f
P1
, as follows:
Select the feedback resistor, R
F
, in the range of 3.3kΩ
to 30kΩ.
Calculate the gain of the modulator (Gain
MOD
)—com-
prised of the regulator’s pulse-width modulator, LC filter,
feedback divider, and associated circuitry—at the desired
crossover frequency, f
CO
, using the following equation:
where V
FB
is the 0.6V (typ) FB_ input-voltage set-point,
L is the value of the regulator inductor, ESR is the
series resistance of the output capacitor, and V
OUT_
is
the desired output voltage.
The gain of the error amplifier (Gain
E/A
) in the midband
frequencies is:
The total loop gain is the product of the modulator gain
and the error amplifier gain at f
CO
and should be set
equal to 1 as follows:
Gain
MOD
x Gain
E/A
= 1
So:
20 log 20 log 0dB
R
R
4 ESR x V
2 f L x V
1
10
R
R
10
4 ESR x V
2 f L x V
F
1
FB
CO OUT_
F
1
FB
CO OUT_
×+× =
×
×
××
=
×
××
π
π
Gain
R [k ]
R [k ]
E/A
F
1
=
Ω
Ω
Gain 4(V/V)
ESR [m ]
2 f [kHz] L[ H]
V [V]
V [V]
MOD
CO
FB
OUT_
××
()
×
Ω
πμ
fff
CO Z1 P1
f
f
2
P1
SW
ff
Z1 LC
f
1
2 ESR C
f
1
2LC
ESR
OUT
LC
OUT
=
××
××
π
π
R
1
V
REF
R
F
FB_
COMP_
V
OUT_
R
2
C
F
C
CF
Figure 5a. Type II Compensation Network
GAIN
(dB)
1ST ASYMPTOTE
(ωR
1
C
F
)
-1
2ND ASYMPTOTE
(R
F
R
1
)
-1
3RD ASYMPTOTE
(ωR
F
C
CF
)
-1
ω (rad/sec)
1ST POLE
(AT ORIGIN)
2ND POLE
(R
F
C
CF
)
-1
1ST ZERO
(R
F
C
F
)
-1
Figure 5b. Type II Compensation Network Response
MAX15021
Dual, 4A/2A, 4MHz, Step-Down
DC-DC Regulator withTracking/
Sequencing Capability
Maxim Integrated | 18www.maximintegrated.com
Solving for R
1
:
where V
FB
is the 0.6V (typ) FB_ input-voltage set-point,
L is the value of the regulator inductor, ESR is the
series resistance of the output capacitor, and V
OUT_
is
the desired output voltage.
1) C
F
is determined from the compensator’s leading
zero, f
Z1
, and R
F
as follows:
2) C
CF
is determined from the compensator’s high-fre-
quency pole, f
P1
, and R
F
as follows:
3) Calculate R
2
using the following equation:
where V
FB
= 0.6V (typ) and V
OUT_
is the output voltage
of the regulator.
Type III: Compensation when fCO < fESR
As indicated above, the position of the output capaci-
tor’s inherent ESR zero is critical in designing an appro-
priate compensation network. When low-ESR ceramic
output capacitors (MLCCs) are used, the ESR zero fre-
quency (f
ESR
) is usually much higher than the desired
crossover frequency (f
CO
). In this case, a type III com-
pensation network is recommended (see Figure 6a).
As shown in Figure 6b, the Type III compensation net-
work introduces two zeros and three poles into the con-
trol loop. The error amplifier has a low-frequency pole
at the origin, two zeros, and two higher frequency poles
at the following frequencies:
Two midband zeros (f
Z1
and f
Z2
) are designed to com-
pensate for the pair of complex poles introduced by the
LC filter.
f
P1
introduces a pole at zero frequency (integrator) for
nulling DC output voltage errors.
f
P1
= at the origin (0Hz)
Depending on the location of the ESR zero (f
ESR
), f
P2
can be used to cancel it, or to provide additional atten-
uation of the high-frequency output ripple.
f
P3
attenuates the high-frequency output ripple.
Since C
CF
<< C
F
then:
f
1
2 R C
P3
FCF
=
××π
f
1
2R CC
1
2R
CC
CC
P3
FFCF
F
FCF
FCF
=
××
()
=
××
×
+
π
π
f
1
2RC
P2
II
=
××π
f
1
2RC
f
1
2C(RR)
Z1
FF
Z2
I1I
=
××
=
×× +
π
π
R[k] R[k]
V [V]
V [V] V [V]
21
FB
OUT_ FB
ΩΩ
CF]
1
2 R [k ] f [kHz]
CF
FP1
[μ
π
=
××Ω
C[F]
1
2 R [k ] f [kHz]
F
FZ1
μ
π
=
××Ω
R [k ]
R [k ] 4 ESR[m ] V [V]
2 f [kHz] L[ H] V [V]
1
FFB
CO OUT_
Ω
ΩΩ
=
×× ×
×××πμ
R
1
V
REF
R
F
FB_
COMP_
V
OUT_
R
2
C
F
C
CF
R
I
C
I
Figure 6a. Type III Compensation Network
GAIN
(dB)
1ST ASYMPTOTE
(ωR
1
C
F
)
-1
3RD ASYMPTOTE
(ωR
F
C
I
)
-1
5TH ASYMPTOTE
(ωR
I
C
CF
)
-1
ω (rad/sec)
1ST POLE
(AT ORIGIN)
2ND POLE
(R
I
C
I
)
-1
3RD POLE
(R
F
C
CF
)
-1
1ST ZERO
(R
F
C
F
)
-1
2ND ASYMPTOTE
R
F
R
1
(
)
1
4TH ASYMPTOTE
R
F
R
I
(
)
2ND ZERO
(R
1
C
I
)
-1
Figure 6b. Type III Compensation Network Response

MAX15021ATI+T

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Description:
Switching Voltage Regulators Dual 4A/2A 4MHz w/Tracking/Seq
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